Simplify to lowest terms. $\dfrac{16}{72}$
Answer: There are several ways to tackle this problem. What is the greatest common factor (GCD) of 16 and 72? $16 = 2\cdot2\cdot2\cdot2$ $72 = 2\cdot2\cdot2\cdot3\cdot3$ $\mbox{GCD}(16, 72) = 2\cdot2\cdot2 = 8$ $\dfrac{16}{72} = \dfrac{2 \cdot 8}{ 9\cdot 8}$ $\hphantom{\dfrac{16}{72}} = \dfrac{2}{9} \cdot \dfrac{8}{8}$ $\hphantom{\dfrac{16}{72}} = \dfrac{2}{9} \cdot 1$ $\hphantom{\dfrac{16}{72}} = \dfrac{2}{9}$ You can also solve this problem by repeatedly breaking the numerator and denominator into common factors. For example: $\dfrac{16}{72}= \dfrac{2\cdot8}{2\cdot36}= \dfrac{2\cdot 2\cdot4}{2\cdot 2\cdot18}= \dfrac{2\cdot 2\cdot 2\cdot2}{2\cdot 2\cdot 2\cdot9}= \dfrac{2}{9}$